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x <- rnorm(10)Gaussian Graphical Models (GGMs) are widely used for exploratory data analysis in various fields such as genomics, ecology, psychometry. In a high-dimensional setting, when the number of variables exceeds the number of observations by several orders of magnitude, the estimation of GGM is a difficult and unstable optimization problem. Clustering of variables or variable selection is often performed prior to GGM estimation. We propose a new method allowing to simultaneously infer a hierarchical clustering structure and the graphs describing the structure of independence at each level of the hierarchy. This method is based on solving a convex optimization problem combining a graphical lasso penalty with a fused type lasso penalty. Results on real and synthetic data are presented.
This document provides a template based on the quarto system for contributions to Computo Computo Team (2021). We show how Python (Perez, Granger, and Hunter 2011) or R (R Core Team 2020) code can be included.
First make sure that you are able to build your manuscript as a regular notebook on your system. Then you can start configure the binder environment.
This section covers basic formatting guidelines. Quarto is a versatile formatting system for authoring HTML based on markdown, integrating \LaTeX and various code block interpreted either via Jupyter or Knitr (and thus deal with Python, R and many other langages). It relies on the Pandoc Markdown markup language.
To render/compile a document, run quarto render. A document will be generated that includes both content as well as the output of any embedded code chunks within the document:
quarto render content.qmd # will render to htmlBold text or italic
But we can also do a numbered list
LaTeX code is natively supported1, which makes it possible to use mathematical formulae:
will render
f(x_1, \dots, x_n; \mu, \sigma^2) = \frac{1}{\sigma \sqrt{2\pi}} \exp{\left(- \frac{1}{2\sigma^2}\sum_{i=1}^n(x_i - \mu)^2\right)}
It is also posible to cross-reference an equation, see Equation 1:
\begin{aligned} D_{x_N} & = \frac12 \left[\begin{array}{cc} x_L^\top & x_N^\top \end{array}\right] \, \left[\begin{array}{cc} L_L & B \\ B^\top & L_N \end{array}\right] \, \left[\begin{array}{c} x_L \\ x_N \end{array}\right] \\ & = \frac12 (x_L^\top L_L x_L + 2 x_N^\top B^\top x_L + x_N^\top L_N x_N), \end{aligned} \tag{1}
Quarto includes a nice support for theorems, with predefined prefix labels for theorems, lemmas, proposition, etc. see this page. Here is a simple example:
Theorem 1 (Strong law of large numbers) The sample average converges almost surely to the expected value:
\overline{X}_n\ \xrightarrow{\text{a.s.}}\ \mu \qquad\textrm{when}\ n \to \infty.
See Theorem 1.
Quarto uses either Jupyter or knitr to render code chunks. This can be triggered in the yaml header, e.g., for Jupyter (should be installed on your computer) use
---
title: "My Document"
author "Jane Doe"
jupyter: python3
---For knitr (R + knitr must be installed on your computer)
---
title: "My Document"
author "Jane Doe"
---You can use Jupyter for Python code and more. And R + KnitR for if you want to mix R with Python (via the package reticulate Ushey, Allaire, and Tang (2020)).
R code (R Core Team 2020) chunks may be embedded as follows:
x <- rnorm(10)---
title: "My Document"
author "Jane Doe"
jupyter: python3
---import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots()
ax.plot(np.arange(10))Plots can be generated as follows:
library("ggplot2")
p <- ggplot(mpg, aes(displ, hwy)) +
geom_point() +
geom_smooth()
pInteractive plots may also be produced in the HTML output of the document:
library("plotly")
ggplotly(p)It is also possible to create figures from static images:
Tables (with label: @tbl-mylabel renders Table 1) can be generated with markdown as follows
| Tables | Are | Cool |
|---|---|---|
| col 1 is | left-aligned | $1600 |
| col 2 is | centered | $12 |
| col 3 is | right-aligned | $1 |
Table can also be generated by some code, for instance with knitr here:
knitr::kable(summary(cars), caption = "Table caption.")| speed | dist | |
|---|---|---|
| Min. : 4.0 | Min. : 2.00 | |
| 1st Qu.:12.0 | 1st Qu.: 26.00 | |
| Median :15.0 | Median : 36.00 | |
| Mean :15.4 | Mean : 42.98 | |
| 3rd Qu.:19.0 | 3rd Qu.: 56.00 | |
| Max. :25.0 | Max. :120.00 |
A solution to typeset pseudocode just like you would do with \LaTeX, yet with HTML output is to rely on the JavaScript peudocode.js. Your pseudocode is written inside a <pre> tag. You need to modify the file includes/pseudocode-footer.html so that the Id of the rendered element match the one in <pre id ="">. The result is as follows:
\begin{algorithm}
\caption{A simple Algorithm}
\begin{algorithmic}
\STATE \textbf{Data}: $\mathcal{X} = \{x_1, \dots, x_n\}$
\STATE optimization parameters: number of iterations $T$, learning rate $\eta$
\STATE \textbf{Result}: output $\mathcal{Y} = \{y_1, \dots, y_n\}$
\PROCEDURE{myproc}{$T$, $\eta$}
\FOR{$t = 0$ \TO $T$}
\STATE do something (and fast please)
\ENDFOR
\ENDPROCEDURE
\end{algorithmic}
\end{algorithm}
References are displayed as footnotes using BibTeX, e.g. [@computo] will be displayed as (Computo Team 2021), where computo is the bibtex key for this specific entry. The bibliographic information is automatically retrieved from the .bib file specified in the header of this document (here: references.bib).
As already (partially) seen, Quarto includes a mecanism similar to the bibliographic references for sections, equations, theorems, figures, lists, etc. Have a look at this page.
Check our mock version of the t-SNE paper for a full and advanced example.
sessionInfo()R version 4.2.1 (2022-06-23 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22000)
Matrix products: default
locale:
[1] LC_COLLATE=French_France.utf8 LC_CTYPE=French_France.utf8
[3] LC_MONETARY=French_France.utf8 LC_NUMERIC=C
[5] LC_TIME=French_France.utf8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] plotly_4.10.0 ggplot2_3.3.6
loaded via a namespace (and not attached):
[1] reticulate_1.25 tidyselect_1.1.2 xfun_0.31 purrr_0.3.4
[5] splines_4.2.1 lattice_0.20-45 colorspace_2.0-3 vctrs_0.4.1
[9] generics_0.1.3 viridisLite_0.4.0 htmltools_0.5.3 yaml_2.3.5
[13] mgcv_1.8-40 utf8_1.2.2 rlang_1.0.4 pillar_1.8.0
[17] glue_1.6.2 withr_2.5.0 DBI_1.1.3 lifecycle_1.0.1
[21] stringr_1.4.0 munsell_0.5.0 gtable_0.3.0 htmlwidgets_1.5.4
[25] evaluate_0.16 labeling_0.4.2 knitr_1.39 fastmap_1.1.0
[29] crosstalk_1.2.0 fansi_1.0.3 highr_0.9 Rcpp_1.0.9
[33] scales_1.2.0 jsonlite_1.8.0 farver_2.1.1 png_0.1-7
[37] digest_0.6.29 stringi_1.7.8 dplyr_1.0.9 grid_4.2.1
[41] cli_3.3.0 tools_4.2.1 magrittr_2.0.3 lazyeval_0.2.2
[45] tibble_3.1.8 tidyr_1.2.0 pkgconfig_2.0.3 Matrix_1.4-1
[49] data.table_1.14.2 assertthat_0.2.1 rmarkdown_2.14 httr_1.4.3
[53] rstudioapi_0.13 R6_2.5.1 nlme_3.1-157 compiler_4.2.1
@article{edmondsanou,christopheambroise,genevièverobin,
author = {Do Edmond Sanou, Christophe Ambroise, Geneviève Robin},
title = {Inference of {Multiscale} {Gaussian} {Graphical} {Model}},
journal = {Computo},
date = {},
url = {https://github.com/desanou/multiscale_glasso},
doi = {xxxx},
langid = {en},
abstract = {Gaussian Graphical Models (GGMs) are widely used for
exploratory data analysis in various fields such as genomics,
ecology, psychometry. In a high-dimensional setting, when the number
of variables exceeds the number of observations by several orders of
magnitude, the estimation of GGM is a difficult and unstable
optimization problem. Clustering of variables or variable selection
is often performed prior to GGM estimation. We propose a new method
allowing to simultaneously infer a hierarchical clustering structure
and the graphs describing the structure of independence at each
level of the hierarchy. This method is based on solving a convex
optimization problem combining a graphical lasso penalty with a
fused type lasso penalty. Results on real and synthetic data are
presented.}
}